2.3.143 Problems 14201 to 14300

Table 2.859: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14201

17399

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

1.477

14202

17453

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\ \end{align*}

1.477

14203

18437

\begin{align*} x^{\prime }&=x+y-\cos \left (t \right ) \\ y^{\prime }&=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -2 \\ \end{align*}

1.477

14204

23541

\begin{align*} 2 x^{2} y^{\prime \prime }+7 x y^{\prime }-3 y&=\frac {\ln \left (x \right )}{x^{2}} \\ \end{align*}

1.477

14205

24563

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=-18 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

1.477

14206

9564

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

1.478

14207

9641

\begin{align*} y+y^{\prime }&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

1.478

14208

16559

\begin{align*} x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y&=0 \\ \end{align*}

1.479

14209

18154

\begin{align*} y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\ \end{align*}

1.479

14210

4438

\begin{align*} y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \\ \end{align*}

1.480

14211

7799

\begin{align*} y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}

1.480

14212

8504

\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.480

14213

8840

\begin{align*} y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}

1.480

14214

10113

\begin{align*} y^{\prime \prime }-x^{2} y-x^{2}&=0 \\ \end{align*}

1.480

14215

22702

\begin{align*} 4 y+y^{\prime \prime }&=8 \cos \left (2 x \right )-4 x \\ \end{align*}

1.480

14216

9903

\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.481

14217

12582

\begin{align*} -6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\ \end{align*}

1.481

14218

19779

\begin{align*} y^{\prime \prime }-2 y y^{\prime }&=0 \\ \end{align*}

1.481

14219

2465

\begin{align*} 2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y&=0 \\ \end{align*}

Series expansion around \(t=0\).

1.482

14220

8757

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y&=0 \\ \end{align*}

1.482

14221

25551

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}

1.482

14222

861

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y&=0 \\ \end{align*}

1.483

14223

15302

\begin{align*} y^{\prime \prime }+y&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.483

14224

19989

\begin{align*} {\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2}&=0 \\ \end{align*}

1.483

14225

570

\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=\delta \left (t -\pi \right )+\delta \left (t -2 \pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

1.484

14226

2591

\begin{align*} y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y&=t +1 \\ \end{align*}

1.484

14227

11871

\begin{align*} y^{\prime }&=\frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y} \\ \end{align*}

1.484

14228

15665

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}

1.484

14229

23302

\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ \end{align*}

1.484

14230

16996

\begin{align*} y^{\prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

1.485

14231

19405

\begin{align*} 3 x^{2} y-y^{3}-\left (3 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}

1.485

14232

3329

\begin{align*} y&=x y^{\prime }-{y^{\prime }}^{{2}/{3}} \\ \end{align*}

1.486

14233

14767

\begin{align*} x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.486

14234

16141

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (-3+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

1.486

14235

1618

\begin{align*} y^{\prime }&=\left (x^{2}+y^{2}\right )^{2} \\ \end{align*}

1.487

14236

6290

\begin{align*} \left (8 x^{4}+10 x^{2}+1\right ) y-4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\ \end{align*}

1.487

14237

7319

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+6 y&=0 \\ \end{align*}

1.487

14238

9400

\begin{align*} 2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.487

14239

20629

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\ \end{align*}

1.487

14240

24789

\begin{align*} x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \\ \end{align*}

1.487

14241

1316

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}

1.488

14242

5662

\begin{align*} 4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \\ \end{align*}

1.488

14243

15279

\begin{align*} x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }&=-5 x+2 y \\ \end{align*}

1.488

14244

16718

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y&=0 \\ \end{align*}

1.488

14245

25565

\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=f \\ \end{align*}

1.488

14246

10115

\begin{align*} y^{\prime \prime }-x^{2} y-x^{4}&=0 \\ \end{align*}

1.490

14247

17133

\begin{align*} y^{\prime }&=-y \\ \end{align*}

1.490

14248

18033

\begin{align*} \left (y^{\prime }-1\right )^{2}&=y^{2} \\ \end{align*}

1.490

14249

26616

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align*}

1.490

14250

23

\begin{align*} y^{\prime }&=y-x +1 \\ \end{align*}

1.491

14251

171

\begin{align*} x^{\prime }&=x-x^{2} \\ x \left (0\right ) &= 2 \\ \end{align*}

1.491

14252

994

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 3 \\ \end{align*}

1.491

14253

22931

\begin{align*} x^{\prime }+3 x-2 y&={\mathrm e}^{-t} \\ y^{\prime }-x+4 y&=\sin \left (2 t \right ) \\ \end{align*}

1.491

14254

25560

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}

1.491

14255

3440

\begin{align*} y^{\prime }&=2 y+{\mathrm e}^{2 t} \\ \end{align*}

1.492

14256

9994

\begin{align*} y^{\prime }&=y \\ \end{align*}

1.492

14257

13753

\begin{align*} x y^{\prime \prime }+\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y&=0 \\ \end{align*}

1.492

14258

21618

\begin{align*} y^{\prime \prime }+2 b y^{\prime }+y&=k \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.492

14259

22848

\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.492

14260

25702

\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= {\mathrm e} \\ \end{align*}

1.492

14261

4182

\begin{align*} y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )}&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.493

14262

10427

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\ \end{align*}

1.493

14263

11327

\begin{align*} y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1}&=0 \\ \end{align*}

1.493

14264

12643

\begin{align*} y^{\prime \prime }&=-\frac {b y}{x^{2} \left (x -a \right )^{2}} \\ \end{align*}

1.493

14265

14047

\begin{align*} \left (2 x y^{\prime }-y\right )^{2}&=8 x^{3} \\ \end{align*}

1.493

14266

5622

\begin{align*} {y^{\prime }}^{3}+a x y^{\prime }-a y&=0 \\ \end{align*}

1.494

14267

8993

\begin{align*} 3 x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.494

14268

20655

\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\ \end{align*}

1.494

14269

63

\begin{align*} y^{\prime }+1&=2 y \\ y \left (1\right ) &= 1 \\ \end{align*}

1.495

14270

9041

\begin{align*} y^{\prime \prime }&=-\frac {1}{2 {y^{\prime }}^{2}} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

1.495

14271

25531

\begin{align*} m y^{\prime \prime }-k y&={\mathrm e}^{i \omega t} \\ \end{align*}

1.495

14272

26854

\begin{align*} 2 y y^{\prime }&=1 \\ \end{align*}

1.495

14273

79

\begin{align*} 2 x y^{\prime }+y&=10 \sqrt {x} \\ \end{align*}

1.496

14274

603

\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}

1.496

14275

1102

\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\ \end{align*}

1.496

14276

25317

\begin{align*} y^{\prime }+4 y&=\delta \left (-3+t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

1.496

14277

27750

\begin{align*} x^{2} y^{\prime \prime }+\ln \left (x \right )^{2} y&=0 \\ \end{align*}

1.496

14278

11762

\begin{align*} 4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}

1.498

14279

13209

\begin{align*} y^{\prime }&=y^{2}+a^{2} x^{2}+b x +c \\ \end{align*}

1.498

14280

13941

\begin{align*} y^{\prime \prime }-\left (a +2 b \,{\mathrm e}^{a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{2 a x} y&=0 \\ \end{align*}

1.498

14281

20644

\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (1-x \right )^{2} \\ \end{align*}

1.498

14282

25962

\begin{align*} y^{\prime \prime }+y^{\prime }&=8 \sin \left (4 x \right ) \\ \end{align*}

1.498

14283

26516

\begin{align*} y^{\prime \prime }+k^{2} y&=k \sin \left (k x +\alpha \right ) \\ \end{align*}

1.498

14284

6872

\begin{align*} u^{\prime }-u^{2}&=\frac {2}{x^{{8}/{3}}} \\ \end{align*}

1.499

14285

14778

\begin{align*} x^{\prime }+y^{\prime }-x-3 y&=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y&=1 \\ \end{align*}

1.499

14286

27505

\begin{align*} x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\ \end{align*}

1.499

14287

104

\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\ \end{align*}

1.500

14288

1119

\begin{align*} -y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= a \\ \end{align*}

1.500

14289

6238

\begin{align*} -\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}

1.500

14290

12339

\begin{align*} y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y&=0 \\ \end{align*}

1.501

14291

12616

\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\ \end{align*}

1.501

14292

14810

\begin{align*} x^{\prime }&=x-y-z \\ y^{\prime }&=x+3 y+z \\ z^{\prime }&=-3 x-6 y+6 z \\ \end{align*}

1.501

14293

20199

\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\ \end{align*}

1.502

14294

20444

\begin{align*} y&=a y^{\prime }+b {y^{\prime }}^{2} \\ \end{align*}

1.502

14295

22844

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.502

14296

16567

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-25 y&=0 \\ \end{align*}

1.503

14297

19490

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-2 y&=0 \\ \end{align*}

1.503

14298

1498

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.505

14299

9909

\begin{align*} x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.505

14300

12982

\begin{align*} 4 y y^{\prime }-4 {y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}

1.505